The 22-year-old's current deal in the French capital is due to expire next June, and it has been suggested that the attacker is not interested in signing an extension with Mauricio Pochettino's side.
Real Madrid have long been considered as the favourites to sign the France international, who has scored 132 goals and registered 61 assists in 171 appearances for PSG.
According to 90min, Los Blancos are set to open talks with PSG over a possible move for the World Cup winner, with the Spanish giants now able to afford his wage demands.
The report claims that the exits of Sergio Ramos and Raphael Varane this summer has freed up room on the wage bill to allow Carlo Ancelotti's side to present a suitable contract offer to the attacker.
PSG are expected to continue to fight to keep hold of Mbappe, but the French giants could lose him on a free transfer next year if an agreement over a new deal cannot be reached.
Les Parisiens are thought to value the former Monaco youngster in excess of £150m despite his contract situation. body check tags ::